Jong Yeoul Park

Controllability of second-order neutral functional differential inclusions in Banach spaces

In this paper, we prove the controllability of second-order neutral functional differential inclusions in Banach spaces. The result are obtained by using the theory of strongly continuous cosine families and a fixed point theorem for condensing maps due to Martelli.

On weak solutions for hyperbolic differential inclusion with discontinuous nonlinearities

Abstract In this paper we study the existence of global weak solutions for hyperbolic differential inclusion with a discontinuous and nonlinear multi-valued term and then investigate the asymptotic behavior of the solutions.

Parametric generalized mixed variational inequalities

In this paper, by using the concept of the resolvent operator, we study the behavior and sensitivity analysis of the solution set for a class of parametric generalized mixed variational inequalities with set-valued mappings.

Existence of solutions for nonlinear inequalities in G-convex spaces

By using a fixed-point theorem in G-convex spaces due to the first author, an existence result for abstract nonlinear inequalities without any monotonicity assumptions is established. As a consequence of our result, we obtain some further generalizations of recent known results. As application, an existence theorem for perturbed saddle point problems is obtained in noncompact G-convex spaces.

Existence of solutions and optimal control problems for hyperbolic hemi-variational inequalities

In this paper we prove the existence of solutions for hyperbolic hemivariational inequalities and then investigate optimal control problems for some convex cost functionals.

Pareto equilibria for constrained multiobjective games in locally L-convex spaces

Abstract In this paper, we introduce and study a class of constrained multiobjective games in locally L -convex spaces without linear structure. A new fixed-point theorem for a family of set-valued mappings and an existence theorem of solutions for a system of quasi-equilibrium problems are first proved in noncompact locally L-convex spaces. As applications, several existence theorems of weighted Nash-equilibria and Pareto equilibria for the constrained multiobjective games are established in noncompact locally L -convex spaces. These theorems improve, unify, and generalize the corresponding results of the multiobjective games in recent literature.

Collectively fixed-point theorems in noncompact G-convex spaces

In this paper, by applying the technique of continuous partition of unity and Tychonoffs fixed-point theorem, some new collectively fixed-point theorems for a family of set-valued mappings defined on the product space of noncompact G-convex spaces are proved. Our theorems improve, unify, and generalize many important collectively fixed-point theorems in recent literature.

Almost periodic solutions of fuzzy systems

We prove the existence of almost periodic solutions and asymptotically almost periodic solutions for the fuzzy functional differential equations. Moreover we consider uniform stable and uniformly asymptotically stable of almost periodic solutions for the fuzzy system.

Pullback attractor for a non-autonomous modified Swift-Hohenberg equation

This paper is concerned with a non-autonomous modified Swift-Hohenberg equation ut+@D^2u+2@Du+au+b|@?u|^2+u^3=g(x,t). It is shown that a pullback attractor exists when its external force has exponential growth. Due to the nonlinear terms b|@?u|^2 and u^3, the estimates are delicate. We overcome this difficulty by imposing the exponential growth condition on the external forcing term g(x,t).

Asymptotic stability of a problem with BalakrishnanTaylor damping and a time delay

In this paper, we investigate the asymptotic stability of the viscoelastic Kirchhoff equation with BalakrishnanTaylor damping and a delay term. We establish general energy decay result by suitable Lyapunov functionals.